How Much of a Rope Can Hang Over a Table Without Sliding?

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SUMMARY

The discussion focuses on determining the maximum fraction of a uniform massive rope that can hang over the edge of a table without sliding, given a coefficient of static friction (Us) between the rope and the table. Participants suggest that the largest fraction may be 1/2 and emphasize the need for a mathematical proof. Key concepts include the force acting on the rope, calculated as F=mg, where g is the acceleration due to gravity (9.81 m/s²), and the importance of constructing a free-body diagram to analyze the forces involved.

PREREQUISITES
  • Understanding of static friction and its coefficient (Us)
  • Basic knowledge of forces and Newton's laws (F=mg)
  • Ability to create and interpret free-body diagrams
  • Familiarity with uniform mass distribution in physics
NEXT STEPS
  • Study the principles of static friction in detail
  • Learn how to construct and analyze free-body diagrams
  • Research mathematical proofs related to equilibrium conditions
  • Explore applications of forces in real-world scenarios involving ropes and pulleys
USEFUL FOR

Students in physics, educators teaching mechanics, and anyone interested in understanding the principles of static friction and equilibrium in physical systems.

frog210293
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Homework Statement



a) If the co efficent of static friction between a table and a uniform massive rope is Us, what fraction of the rope can hang over the edge of the table without the rope sliding?


Homework Equations



F=mg

The Attempt at a Solution



The largest fraction of the rope able to overhang would be 1/2?, how would you go about proving that mathematically?

The force on the rope hanging down would be F=m*9.81

where to go from here?
 
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Make the free-body diagram for both pieces of the rope (hanging and resting on the table). Find the condition when it just starts to slide.

ehild
 

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